Three taps $A, B$ and $C$ fill a tank in $20$ min,$15$ min and $12$ min,respectively. If all the taps are opened simultaneously,how long will they take to fill $40 \%$ of the tank (in $min$)?

One tap can fill a cistern in $2$ hours and another can empty the cistern in $3$ hours. How long will it take to fill the cistern if both the taps are opened (in $\text{hours}$)?

Pipe $A$ can fill a tank in $30$ minutes,while pipe $B$ can fill the same tank in $10$ minutes and pipe $C$ can empty the full tank in $40$ minutes. If all the pipes are opened together,how much time will be needed to make the tank full?

Having the same capacity,$9$ taps fill up a water tank in $20$ minutes. How many taps of the same capacity are required to fill up the same water tank in $15$ minutes?

If pipe $P$ can fill a tank in $p$ hours and pipe $Q$ can empty the same tank in $q$ hours (where $q > p$),and both pipes are opened simultaneously,in how many hours $(r)$ will the tank be filled?

Pipe $A$ can fill a tank in $5$ $hours$,pipe $B$ in $10$ $hours$,and pipe $C$ in $30$ $hours$. If all the pipes are opened,in how many $hours$ will the tank be filled?